Set AutoPostBack true for DropDownList1 and DropDownList2 as you did in DropDownList3 as below
<br /><asp:DropDownList ID="DropDownList1" runat="server" Visible="false" AutoPostBack="True" onSelectedIndexChanged="nextStep" ></asp:DropDownList><br /><br /><asp:DropDownList ID="DropDownList2" runat="server" Visible="false" AutoPostBack="True" onSelectedIndexChanged="nextStep" ></asp:DropDownList><br /><br />